Petroleum companies frequently use seismic surveys in their search for exploitable petroleum reservoirs. A seismic survey is an attempt to map the subsurface of the earth by sending sound energy down into the ground and recording the “echoes” that return from the rock layers below. The source of the down-going sound energy might come from explosions or seismic vibrators on land, and air guns in marine environments. During a seismic survey, the energy source is moved across the surface of the earth above the geologic formations of interest. Each time the source is triggered, it generates a seismic signal that travels downward through the earth and is partially reflected from boundaries between different rock types. These reflections cause sound energy waves to return toward the surface where they are detected by a set of spaced geophones or seismic energy receivers. The receivers generate electrical signals representative of the sound energy arriving at their locations.
The acoustic energy detected by the seismic receivers is generally amplified and then recorded or stored in either analog or digital form on some storage medium. The recording is made as a function of time after the triggering of the source. The recorded data may be transported to a computer and displayed in the form of traces, i.e., plots of the amplitude of the reflected seismic energy as a function of time for each of the geophones or seismic energy receivers. Such displays or data subsequently undergo additional processing to simplify the interpretation of the  arriving acoustic energy at each seismic receiver in terms of the subsurface layering of the earth's structure. Data from multiple explosion/recording location combinations are combined to create a nearly continuous profile of the subsurface that may extend for many miles.
Survey types are often distinguished in terms of the pattern of recording locations on the earth's surface. As viewed from above, the recording locations may be laid out in a (one-dimensional) straight line, in which case the result is a two-dimensional (2-D) seismic survey. A 2-D survey can be thought of as a cross-sectional view (a vertical slice) of the earth formations lying underneath the line of recording locations. Alternatively, the recording locations may be laid out in a two-dimensional pattern on the surface, in which case the result is a three-dimensional (3-D) seismic survey. A 3-D survey produces a data “cube” or volume that is, at least conceptually, a 3-D picture of the subsurface that lies beneath the survey area.
3-D seismic surveys have become commonplace due to the comprehensive information they provide about the earth's subsurface. 3-D seismic surveys are generally performed using what is called the “swath method”. In using the swath method on land, a number of very long (e.g., on the order of 3000-30,000 feet) receiver lines, each containing uniformly spaced receivers, are placed in parallel on the surface above and around the subsurface formations to be surveyed. Limitations on the data recording equipment and other economic considerations frequently limit the number of receiver lines and the number of receivers on each line that can be used to perform the survey. After the receiver lines have been placed, a seismic source is activated at each of various uniformly spaced locations (source stations) to impart desired shock waves into the earth.
The spot halfway between the source and a receiver (the “midpoint”) has a particular significance in seismic surveys. If the subsurface formations were made up of flat layers parallel to the seismic source/receiver arrangement, the receiver's response to a firing of the source represents the reflections from formations directly below the midpoint. Even when subsurface formations do not adhere to the ideal, the reflections from below the midpoint can be reinforced and extraneous reflections (and random noise) can be attenuated by “stacking” receiver responses that share a common midpoint. Stacking involves time-scaling the receiver responses to account for travel time differences (e.g., when one source-receiver pair is more widely spaced than another), and averaging the results. Prestack processing and interpolation techniques may also be employed, depending upon the nature of the seismic data and the targets under investigation. Migration processing techniques may also be employed to further refine and enhance the acquired data. 
To enable stacking, existing 3-D seismic survey methods design the seismic receiver point arrangement and the pattern of source firings in a manner that causes many source-receiver pairs to share common midpoints. The number of receiver responses sharing a common midpoint is known as the multiplicity, or “fold”, so that, e.g., four receiver responses sharing a common midpoint represent a four-fold response at that midpoint. In existing seismic survey methods, the receivers and source firings are arranged in uniformly spaced grids to maximize the fold in view of the desired resolution and various constraints on the number of receivers and source firings.
The receiver point arrangement may be used to define the survey coordinate system, with the direction of the receiver lines being termed the “inline” direction, and the direction perpendicular to the receiver lines being termed the “crossline” direction. Generally, the survey volume is divided into constituent “bins” having a length and a width based on the desired resolution of the resulting 3-D picture. The length and width of the bins are determined by the source and receiver spacings. Within the horizontal extent defined by the length and width of a bin, existing survey methods provide a single common midpoint where the receiver responses may be stacked to maximize the fold.
In U.S. Pat. No. 5,402,391, Cordsen discloses a method of distributing midpoints more evenly within a constituent bin to enable a finer-grained optimization between fold (signal-to-noise ratio) and resolution. As disclosed therein, the distributed midpoints can be combined in different groupings, with larger groupings having increased fold (higher signal-to-noise ratio) at the cost of a larger bin size (lower resolution). This enhanced flexibility may provide insurance, enabling survey data to still be used with acceptable spatial resolution even when survey conditions were noisier than anticipated. In U.S. Pat. No. 5,511,039, Flentge discloses an alternative method of providing such a distribution of midpoints within constituent bins (herein termed “bin fractionation”). Further, bins could be similarly fractionated by using variable intervals between adjacent source or receiver points. However, with current recording systems and methodologies, such techniques would not be deemed efficient for field acquisition.
In both the Cordsen and Flenge methods, the receivers and source firings are maintained in straight lines and at regular intervals along those lines. In some cases, such straight lines can be undesirable. For example, in forested or jungle areas, some clearing of growth may be needed to lay out the receiver strings. When the receiver lines or source lines are straight, the resulting cuts  in the forest may extend for miles in straight lines. Such cuts create undesirable environmental impact by creating sightlines that encourage public access to isolated areas.
Thus, a need exists for an alternative bin fractionation method for three-dimensional seismic surveys.